29.10.22 problem 288

Internal problem ID [4888]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 288
Date solved : Monday, January 27, 2025 at 09:46:34 AM
CAS classification : [_separable]

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+2 y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

dsolve((-x^2+1)*diff(y(x),x)+2*x*y(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} x^{2}-c_{1} \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 18

DSolve[(1-x^2)D[y[x],x]+2 x y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 \left (x^2-1\right ) \\ y(x)\to 0 \\ \end{align*}